Calculus question, 10 points?

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In the short run, the only input into production that is considered to be adjustable is the number of laborers. In the long term, the amount of plant and equipment can be adjusted. Finally, in the very long run the technological possibilities available to the company can be changed. In this project, you will be examining a certain company where the number of laborers can be varied.
Your company titled BANGALORES R US produces bangalore torpedoes (commonly called bangalores,) a demolition used for breaching wire obstacles and mines. It produces these devices for the Army Corps of Engineers according to the production function Q = 12L+ 29L2-1.1L3, where Q is the number of bangalores produced per year and L is the number of laborers used per year for production. Additionally, the price of labor and other consumable materials (PL) is $7000 per laborer year. Each bangalore sells for $125.
For all functions "L" should be considered the independent variable.


7. Economists refer to marginal revenue (MR) as the change in total revenue attributable to a one-unit change in output. The marginal cost (MC) is the change in total cost attributable to a one-unit change in output. In other words, marginal revenue is directly related to the derivative of the total revenue function and marginal cost is directly related to the derivative of the total cost function. Using your work above, explain why economists use the equation MR = MC to maximize profits.
8. "The law of diminishing returns states that if increasing amounts of a variable factor (in this case, laborers) are applied to a production line, eventually a situation will be reached in which each additional unit of the variable factor adds less to the total production than the previous unit." Explain where the point of diminishing returns for the laborers is and why. What is a physical explanation in your company for the point of diminishing returns?